[kwantam]

"Pick a random odd number and keep adding 2 until you find a prime" is, perhaps unintuitively, essentially fine for RSA key generation---under mild conditions, the security loss is single-digit bits at best. See Abboud and Prest, "Cryptographic Divergences: New Techniques and New Applications", SCN 2020 [1], Section 4.1.

(This is a relatively recent result. And as I mentioned in my other comment, this is not a defense of the article!)

[1] https://eprint.iacr.org/2020/815

[throwaway81523]

Interesting. I'll look when I get a chance, but it sounds like deep math. The distribution of primes empirically seems well approximated by Cramér's random model, but it's incredibly hard to know anything for certain. For example, whether there are infinitely many twin primes is a famous open problem.